The extension of the multiple-reflection theory to take account of absorption at the edges of the cavity between the septa of a double panel is described, and an expression is obtained for the random incidence transmission loss of a double panel with edge absorption, given values of the panel dimensions and edge absorption coefficient. A curve is given of the measured random incidence transmission loss of a thin double aluminium panel with glass fibre absorbent around the edge of the cavity and theoretical curves given for the same panel with different values of the edge absorption coefficient. From the curves it is inferred that using a value of the edge absorption coefficient of unity in the theory, gives the best agreement between theory and experiment. A curve of the measured transmission loss of a thin polythene panel with glass fibre absorbent around the cavity edges and a theoretical curve with the absorption coefficient equal to unity are given. Good agreement between experiment and theory is obtained without the somewhat unrealistic assumptions of our previous paper. The effect of truncation of multiple reflections between the septa of a double panel upon the “mass-spring-mass” resonance is considered, and the finite panel theory is compared to modal theory.